對數平方怎么處理？
對數的性質及推導
定義：
若a^n=b(a>0且a≠1)
則n=log(a)(b)
根本性質：
1、a^(log(a)(b))=b
2、log(a)(a^b)=b
3、log(a)(MN)=log(a)(M)+log(a)(N);
4、log(a)(M÷N)=log(a)(M)-log(a)(N);
5、log(a)(M^n)=nlog(a)(M)
6、log(a^n)M=1/nlog(a)(M)
推導
1、由于n=log(a)(b)，代入則a^n=b，即a^(log(a)(b))=b。
2、由于a^b=a^b
令t=a^b
所以a^b=t，b=log(a)(t)=log(a)(a^b)
3、MN=M×N
由根本性質1(換掉M和N)
a^[log(a)(MN)] = a^[log(a)(M)]×a^[log(a)(N)]
由指數的性質a^[log(a)(MN)] = a^{[log(a)(M)] + [log(a)(N)]}
又由于指數函數是單調函數，所以
log(a)(MN) = log(a)(M) + log(a)(N)
4、與（3）相似處置
MN=M÷N
由根本性質1(換掉M和N)
a^[log(a)(M÷N)] = a^[log(a)(M)]÷a^[log(a)(N)]
由指數的性質
a^[log(a)(M÷N)] = a^{[log(a)(M)] - [log(a)(N)]}
又由于指數函數是單調函數，所以
log(a)(M÷N) = log(a)(M) - log(a)(N)
5、與（3）相似處置
M^n=M^n
由根本性質1(換掉M)
a^[log(a)(M^n)] = {a^[log(a)(M)]}^n
由指數的性質
a^[log(a)(M^n)] = a^{[log(a)(M)]*n}
又由于指數函數是單調函數，所以
log(a)(M^n)=nlog(a)(M)
根本性質4推行
log(a^n)(b^m)=m/n*[log(a)(b)]
推導如下：
由換底公式（換底公式見下面）[lnx是log(e)(x)，e稱作自然對數的底]
log(a^n)(b^m)=ln(b^m)÷ln(a^n)
換底公式的推導：
設e^x=b^m,e^y=a^n
則log(a^n)(b^m)=log(e^y)(e^x)=x/y
x=ln(b^m),y=ln(a^n)
得：log(a^n)(b^m)=ln(b^m)÷ln(a^n)
由根本性質4可得
log(a^n)(b^m) = [m×ln(b)]÷[n×ln(a)] = (m÷n)×{[ln(b)]÷[ln(a)]}
再由換底公式
log(a^n)(b^m)=m÷n×[log(a)(b)] -